The proofs are given in subsection:proof-hn and
subsubsection:corollary-proof.
This latter corollary salvages the main theorem of [1]} in the
case of vector bundles of low rank when \(E_\star \)  is given the parabolic
structure associated to \(\nabla \) ; it salvages the main theorem of
[2]} in low rank when \(E_\star \)  is given the trivial parabolic structure (in which case it agrees with cor:stable).
